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Stopped Compound Poisson Process and Related Distributions

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Advances in Distribution Theory, Order Statistics, and Inference

Part of the book series: Statistics for Industry and Technology ((SIT))

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Abstract

This chapter considers the first-crossing problem of a compound Poisson process with positive integer-valued jumps in a nondecreasing lower boundary. The cases where the boundary is a given linear function, a standard renewal process, or an arbitrary deterministic function are successively examined. Our interest is focused on the exact distribution of the first-crossing level (or time) of the compound Poisson process. It is shown that, in all cases, this law has a simple remarkable form which relies on an underlying polynomial structure. The impact of a raise of a lower deterministic boundary is also discussed.

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Author information

Authors and Affiliations

  1. Université Libre de Bruxelles, Bruxelles, Belgium

    Claude Lefèvre

Authors
  1. Claude Lefèvre
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

    N. Balakrishnan

  2. Department of Economics, University of Cantabria, s/n Avenida de los Castros, Santander, 39005, Spain

    José María Sarabia  & Enrique Castillo  & 

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© 2006 Birkhäuser Boston

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Lefèvre, C. (2006). Stopped Compound Poisson Process and Related Distributions. In: Balakrishnan, N., Sarabia, J.M., Castillo, E. (eds) Advances in Distribution Theory, Order Statistics, and Inference. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4487-3_2

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